A147583 Number of partitions of n into distinct parts such that 5*u<=v for all pairs (u,v) of parts with u

1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 7, 7, 7, 7, 7, 8, 9, 9, 9, 9, 9, 10, 11, 11, 11, 11, 11, 12, 13, 13, 13, 13, 13, 14, 15, 15, 15, 15, 15, 16, 17, 18, 18, 18, 18, 19, 20, 21, 21, 21, 21, 22, 23, 24, 24, 24, 24, 25, 26, 27, 27, 27, 27

Offset: 1

Author

Reinhard Zumkeller, following a suggestion of Clark Hanley (clark.hanley(AT)gmx.com), Nov 08 2008

Keywords

• nonn

Comments

From Edward Early, Jan 10 2009: (Start)

Also the dimension of the n-th degree part of the mod 5 Steenrod algebra.

Also the number of partitions into parts (5^j-1)/4=1+5+5^2+...+5^(j-1) for j>=1. (End)

Examples

			a(29) = #{29,28+1,27+2,26+3,25+4} = 5;
a(30) = #{30,29+1,28+2,27+3,26+4,25+5} = 6;
a(31) = #{31,30+1,29+2,28+3,27+4,26+5,25+5+1} = 7.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000041, A000009, A000929, A132011.

Programs

Haskell

a147583 = p [1..] where
   p _      0 = 1
   p (k:ks) m = if m < k then 0 else p [5 * k ..] (m - k) + p ks m
-- Reinhard Zumkeller, Oct 10 2013